A conventionally known method for estimating a vehicle speed is disclosed, for example, in Japanese Patent Publication No. 6902/1981. With this method, the vehicle speed is approximated according to the maximum deceleration intrinsic for the vehicle when the vehicle is decelerating. According to this method, a presumed vehicle speed, which is close to the actual vehicle speed, can be obtained while the vehicle is traveling on a road surface which exhibits a maximum deceleration. However, as shown in FIG. 3, the accuracy of the presumed vehicle speed V, with respect to the actual vehicle speed V', deteriorates when the vehicle is on a road surface having a low vehicle deceleration, so that the start of an antilock brake control tends to be delayed due to the deterioration of the accuracy between the estimated speed and the actual speed.